Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Léger, Tristan"'
Autor:
Ampatzoglou, Ioakeim, Léger, Tristan
In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schr\"{o}dinger models. We show well-posedness using a collisional averaging estimate proved in our earlier work \cit
Externí odkaz:
http://arxiv.org/abs/2411.12868
Autor:
Ampatzoglou, Ioakeim, Léger, Tristan
In this paper we construct global strong dispersive solutions to the space inhomogeneous kinetic wave equation (KWE) which propagate $L^1_{xv}$ -- moments and conserve mass, momentum and energy. We prove that they scatter, and that the wave operators
Externí odkaz:
http://arxiv.org/abs/2408.05818
In this paper, we prove $L^2 \to L^p$ estimates, where $p>2$, for spectral projectors on a wide class of hyperbolic surfaces. More precisely, we consider projections in small spectral windows $[\lambda-\eta,\lambda+\eta]$ on geometrically finite hype
Externí odkaz:
http://arxiv.org/abs/2306.12827
Autor:
Léger, Tristan, Pusateri, Fabio
This note complements the paper \cite{LP} by proving a scattering statement for solutions of nonlinear Klein-Gordon equations with an internal mode in $3$d. We show that small solutions exhibit growth around a one-dimensional set in frequency space a
Externí odkaz:
http://arxiv.org/abs/2203.05694
Autor:
Léger, Tristan, Pusateri, Fabio
We consider Klein-Gordon equations with an external potential $V$ and a quadratic nonlinearity in $3+1$ space dimensions. We assume that $V$ is regular and decaying and that the (massive) Schr\"odinger operator $H=-\Delta+V+m^2$ has a positive eigenv
Externí odkaz:
http://arxiv.org/abs/2112.13163
Autor:
Germain, Pierre, Léger, Tristan
We develop a unified approach to proving $L^p-L^q$ boundedness of spectral projectors, the resolvent of the Laplace-Beltrami operator and its derivative on $\mathbb{H}^d.$ In the case of spectral projectors, and when $p$ and $q$ are in duality, the d
Externí odkaz:
http://arxiv.org/abs/2104.04126
We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existence of small shrinkers.
Externí odkaz:
http://arxiv.org/abs/1911.03544
This article is devoted to backward self-similar blow up solutions of the compressible Navier-Stokes equations with radial symmetry. We show that such solutions cannot exist if they either satisfy an appropriate smallness condition, or have finite en
Externí odkaz:
http://arxiv.org/abs/1911.00339
Autor:
Germain, Pierre, Léger, Tristan
Publikováno v:
In Journal of Functional Analysis 15 July 2023 285(2)
Autor:
Léger, Tristan
In this paper we study the asymptotic behavior of a quadratic Schr\"{o}dinger equation with electromagnetic potentials. We prove that small solutions scatter. The proof builds on earlier work of the author for quadratic NLS with a non magnetic potent
Externí odkaz:
http://arxiv.org/abs/1903.09838